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Recently developed techniques have made it possible to quickly learn ac-curate probability density functions from data in low-dimensional continu-ous spaces. In particular, mixtures of Gaussians can be fitted to data very quickly using an accelerated EM algorithm that employs multiresolution kd-trees (Moore, 1999). In this paper, we propose a kind of Bayesian network in which low-dimensional mixtures of Gaussians over different subsets of the domain's variables are combined into a coherent joint probability model over the entire domain. The network is also capable of modelling complex depen-dencies between discrete variables and continuous variables without requiring discretization of the continuous variables. We present efficient heuristic al-gorithms for automatically learning these networks from data, and perform comparative experiments illustrating how well these networks model real sci-entific data and synthetic data. We also briefly discuss some possible im-provements to the networks, as well as their possible application to anomaly detection, classification, probabilistic inference, and compression.